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C2×C3×ΓL(1,𝔽8)⋊D47 #26044918

order11844
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×ΓL(1,𝔽8)⋊D47
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C3×D47)
unambiguous semidirect product(C2×C47)⋊(C3×AGL(1,𝔽7))
unambiguous semidirect product(C2×D329)⋊C32
unambiguous semidirect product(C2×C3×D329)⋊C3

Splittings

Fitting, socleC2×C3×C7×C47 ⋊ C2×C3
derived, HallC7×C47 ⋊ C22×C32
HallC3×ΓL(1,𝔽8)×C47 ⋊ C22
HallC2×D329 ⋊ C32
HallC3×ΓL(1,𝔽8) ⋊ C2×D47
SylowC47 ⋊ C2×C3×AGL(1,𝔽7)
SylowC7 ⋊ C2×C32×D47

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)⋊D47
commutator, cosocle, hypocenterC7×C47C22×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C47C2×C3
LCSG ▷ C7×C47
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

732 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 65);